Boolean difference leaves open gap
Booleans ussually fails on non-manifold mesh.
To see these problematic parts - from within Edit Mode, using Vertex selection, with no geometry selected, Search for &quot;manifold&quot; (Select non-manifold operation appear). For more info see Blender Manual

Q: Is there a way to 'fill' model and make it completely solid?
A: In a meaning - closed mesh without holes - Yes
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Fill
Search for Fill operator and increase number of vertices in tool properties until the holes are filled. Like here it was value 14.

But N-gons are not the best for boolean operations so probably better to try ...
Grid Fill
Like here. Important for this function is to have a loop of even number of vertices. If you don't have, you can select one edge and subdivide it.
(White vertex in the screen is one I added.)

Or even better to Triangulate whole mesh Ctrl+T
Remesh
Or you can try Remesh modifier &gt; Sharp if there is too much work, but even on hi Octree Depth in wouldn't be precise.